Mathematical model of solid tumor formation

The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical tumours, the points of the beginning and the end of spherical growth, and the further development of complex structures (elongated outgrowths, dendritic structures, and metastases) are derived from the assumption that the reproduction rate of a population of cancer cells is a non-monotone function of their local concentration. The predicted statistical distribution of the characteristic tumour sizes, when compared to the clinical data, will make a basis for checking the validity of the theory. 1. Introduction Tumour growth modelling has been the subject of much recent literature (e.g., [1-12]), but the existing mathematical models appear to neglect the local interaction between cancer and tissue cells. This interaction between cancer and tissue cells affects the cancer cells' reproduction rate the way that it becomes dependent on their local concentration [13-17]. Therefore, tumour growth is mainly determined by the behaviour of cancer cells adjacent to the tumour surface. This process, in its turn, is largely dependent on the tumour's local curvature. We apply this approach to investigate the macroscopic effects of tumour growth in a homogeneous tissue. The effects of local interaction can be most simply described using the reproduction function approach. Figure 1 shows hypothetical non-monotone curves 1-3 describing the reproduction rate of cancer cells vs. local